Across their comedy careers, Jon Stewart and Robert Smigel have taken wildly different approaches to topical humor. Mr. Stewart, as the host of “The Daily Show,” honed a pointed, partisan perspective that rooted out hypocrisy in current events. Mr. Smigel has developed a gleefully unmannered voice that he’s used to send up politics and pop culture on shows like “Saturday Night Live” and as his trash-talking puppet creation, Triumph the Insult Comic Dog.

The two friends recently spoke about their views of the current political moment as they prepare for their annual comedy concert, “Night of Too Many Stars: America Unites For Autism Programs,” to benefit Next for Autism, which creates and supports school programs and services for people with autism. This year’s event will be held on Saturday at the Theater at Madison Square Garden and broadcast live on HBO, with a lineup that includes Chris Rock, Stephen Colbert, Adam Sandler, Abbi Jacobson and Hasan Minhaj.

This interview occurred before The New York Times published a report on the sexual misconduct of Louis C.K., who was scheduled to perform at the benefit. HBO has since announced that he has been dropped from the lineup. In a statement provided after the interview, Mr. Stewart and Mr. Smigel said: “It’s obviously very upsetting, and we hope the victims are finding some solace. We’re thankful that the culture’s finally changing and allowing them to feel safe enough to speak out.”

The show comes at a challenging moment for comedy, which is having a hard time preserving an inclusive, big-tent spirit when performers feel compelled to express their personal politics in their work. Mr. Stewart and Mr. Smigel got together recently to talk about “Night of Too Many Stars” and how comedy has been affected by internet culture and polarization. These are edited excerpts from that conversation.

When did you two first meet?

JON STEWART Hebrew school.

ROBERT SMIGEL Summer camp. We were in “Godspell” together. I think I met you at an “S.N.L.” party.

STEWART Those were always the parties that you’d walk outside and go, it’s light again.

SMIGEL The first benefit my wife, Michelle, and I did for NBC was in 2003. Everybody who does the show, they’re happy to help and I’m very grateful. Jon was really curious, and when I told him why this exists, it was because my son Daniel couldn’t get into any kind of school that could help him at that age.

STEWART When you see people that you admire, you have this idea that they can solve anything that comes their way. To hear about what he was dealing with and how much they had to move heaven and earth, just to get basic necessities, it was shocking.

Are you concerned that the political leanings of some performers — Jon, Stephen Colbert, John Oliver — might discourage some of the viewers you’re trying to reach?

SMIGEL Hopefully people won’t take it out on people with autism.

STEWART “I didn’t like that joke, so this school goes unfunded.”

SMIGEL We’re going to try not to be too divisive.

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The “Night of Too Many Stars” benefit has in past years rounded up some of the big names in comedy, like Stephen Colbert, left, and Steve Carell, right.CreditCharles Sykes/Associated Press

Is it harder now to put together a comedy event intended for a wide audience? Is it possible to be a comedian without a political point of view?

STEWART [old man voice] “It was a simpler time. A movie was a nickel. A sandwich, they paid you to eat.” Now everything is conflict. Everything exists now for clicks. You’re incentivized to pick not just the lowest-hanging fruit but the fruit that tastes the worst. Because what you want is a reaction, whether it be incredibly positive or incredibly negative. You can’t avoid that that is the world in which this is born, or even a world that we helped create.

Do you think you contributed to that environment? Do you feel responsible for ——

STEWART For the sad state of the world? I do, but not for that reason. I just assume I’m always doing something wrong. Some of it is that the news cycle is so relentless and ubiquitous. Comedy shows that are promoting more day-and-date stuff have to keep up with that.

SMIGEL Since Jon started, comedy has had to deal with the instant reaction it gets on the web. What frustrates me is seeing comedy succumbing to that. A lot of times, jokes now are judged on the target — on the point of view, rather than how funny they are.

Has the internet made people quicker to take offense at jokes?

STEWART I don’t think they’re quicker to offense. I think it’s quicker that you know about it. The outrage has always been there — it just wasn’t on your feed.

SMIGEL I did these Triumph specials last year, and by the time the election ended I was just like, “Enough.” I was so disgusted by both sides. I was supporting Hillary, but all she would talk about in emails I would get is that Trump is a misogynist. No policy stuff. Just that urge to be divisive and to call the other side names, I was happy to sit it out.

STEWART Exactly. That’s our job, to call these people names! Their job is to take it!

STEWART In certain moments it leaves a mark. You see that it does leave permanent scars in its wake, in very rare instances. But there was that PR person, Justine Sacco, who had tweeted out a bad joke about AIDS and traveling to South Africa. By the time she got off the plane, her life was over. And she was just a civilian in the culture war, to a large extent.

SMIGEL You forget that this person who might have made a mistake on Twitter was maybe not 100 percent evil and worthy of losing everything.

STEWART I think that I contributed to that culture. I took a long, hard look at that idea of unfairness and context. I felt like we [“The Daily Show”] worked really hard to maintain that credibility. But there’s no question that it influenced and partook sometimes in a dehumanizing process. No question. Even with situations like Anthony Weiner. When the pile-on occurs, that person turns into a two-dimensional Flat Stanley, as everybody pounds on them. And then that person ends up, actually, turning out to be horrible and has to go to jail. [laughter]

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Mr. Stewart, here with Mr. Smigel, has no patience for people who wish we could go back to the more politically evenhanded comedy of Johnny Carson.CreditBryan Derballa for The New York Times

Knowing this capacity for outrage exists, are you more wary, as comedians, about what you say in your performances?

STEWART We’re not victims of this culture, by any stretch of the imagination, and those comments are the price of doing business in the cultural sphere.

SMIGEL What bothers me is that temptation to fuel your side’s fire; it’s on both sides, more than ever. I don’t want to be part of that problem. There was a point where I was like, O.K., this guy’s been elected. Now if I keep relentlessly hitting him with my puppet, am I really being helpful? Or am I just profiting?

For people who don’t share your politics and feel alienated by what they see in TV comedy — who wish we could go back to a more evenhanded era of Johnny Carson — do they have a point?

STEWART Here’s what I would say: Tough shit. Honestly. The idea that you’ve lost the pleasure of watching Carson? We all have lost that pleasure. I used to like watching Carson, too. But I think that’s a cop-out. The people that say, “This culture isn’t for me,” live in a nostalgic world. Those are the people that are the first to tell minorities, “Suck it up.” Those are the first people to say to individuals that are being relentlessly either ostracized or legally threatened, “Oh, snowflake, watch yourself.” But God forbid somebody doesn’t say “Merry Christmas.” It’s the empty rhetoric of grievance, and I don’t feel bad in any way, whatsoever.

SMIGEL Colbert, especially, is hilarious, night in and night out. Sarah [Silverman]’s trying really hard. She’s doing a show on Hulu where she’s really trying to engage with people, and face them as human beings. I want Colbert to keep doing what he’s doing, but I want to see more people make that effort, too. Because we need both.